Sparse domination for q-variation associated with functional calculus

@misc{chen2026sparse,
  title = {{Sparse domination for $q$-variation associated with functional calculus}},
  author = {Yanhan Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38711},
  eprint = {2610.38711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38711},
}

TY  - UNPB
TI  - Sparse domination for q-variation associated with functional calculus
AU  - Yanhan Chen
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38711
UR  - https://arxiv.org/abs/2610.38711
AB  - We establish sparse domination for the q-variation of functional calculus families {φ(tL)}_t>0 on spaces of homogeneous type. Under generalized Gaussian estimates, we consider holomorphic multipliers of injective accretive operators, and Sobolev-type spectral multipliers of non-negative self-adjoint operators. For the Sobolev-type multipliers, we show that our regularity assumption is sharp in general except the endpoint. As corollaries, we obtain weighted q-variational estimates for Bochner-Riesz means and regularized Schrödinger groups. Finally, we give several examples of operators to which our results apply.
ER  -